Physical mechanism of grain refinement in solidification of undercooled melts

Modeling of dendrite arm fragmentation and dendrite arm coarsening⋆

A two-dimensional quantitative cellular automaton (CA) model is employed to simulate dendrite arm fragmentation and dendrite arm coarsening in mushy zones. The phenomenon of dendrite arm fragmentation of an Al-Cu alloy during heating is well represented by the CA simulation, and it is analyzed in detail by comparing the local actual concentration and local equilibrium concentration. The CA simulations for the dendritic microstructures of SCN-ACE alloys during isothermal holding in a mushy zone reproduce the typical dendrite coarsening features as observed in experiments. The effects of holding temperature and alloy composition on the microstructures and dendrite coarsening kinetics are investigated. It is found that the melting of small dendrite arms and interdendritic groove advancement are the two main mechanisms in dendrite coarsening. The mechanism of coalescence by joining arm tips is more likely to take place at a lower temperature or for a lower alloy composition, while the dendrite arm fragmentation mechanism tends to occur at a higher temperature. The coarsening rate constant is found to decrease with increasing holding temperature and alloy composition.

Particle Compression Test: A Key Step towards Tailoring of Feedstock Powder for Cold Spraying

Cold spray is on the way to becoming a mainstream technology for coating and additive manufacturing processes. While there have been many advances in various aspects of this technology, the question of tailoring the ‘ideal’ feedstock powder for cold spraying has remained open. In particular, the mechanical strength and its dependence on the particle size, which are amongst the most relevant properties of the feedstock powder for cold spraying, are rarely covered when reporting powder specifications. This is mainly because of the lack of standardised methods of characterisation for these specific properties. In the present case study, we demonstrate how compression tests of single Inconel 718 particles by using a modified nanoindenter can address this central question. Data analyses are supported by finite element modelling of particle compression for a range of plastic behaviours. The results of simulation are then stored in the form of a surrogate model for subsequent comparison with the experimental data. Thus, the ultimate tensile strength and the size of the examined particles are calculated directly from the measured force-displacement data. The paper will also discuss how this information can be used to optimise cold spraying, and so, unveils a key step towards the design and manufacturing of cold-spray-specific feedstock powder.

Modeling of dendrite growth from undercooled nickel melt: sharp interface model versus enthalpy method

The dendritic growth of pure materials in undercooled melts is critical to understanding the fundamentals of solidification. This work investigates two new insights, the first is an advanced definition for the two-dimensional stability criterion of dendritic growth and the second is the viability of the enthalpy method as a numerical model. In both cases, the aim is to accurately predict dendritic growth behavior over a wide range of undercooling. An adaptive cell size method is introduced into the enthalpy method to mitigate against 'narrow-band features' that can introduce significant error. By using this technique an excellent agreement is found between the enthalpy method and the analytic theory for solidification of pure nickel.

Dendrite fragmentation induced by massive-like δ-γ transformation in Fe-C alloys

Dendrite arm fragmentation is considered in solidification structure tailoring. Time-resolved and in situ imaging using synchrotron radiation X-rays allows the observation of dendrite arm fragmentation in Fe-C alloys. Here we report a dendrite arm fragmentation mechanism. A massive-like transformation from ferrite to austenite rather than the peritectic reaction occurs during or after ferrite solidification. The transformation produces refined austenite grains and ferrite-austenite boundaries in dendrite arms. The austenite grains are fragmented by the liquid phase that is produced at the grain boundary. In unidirectional solidification, a slight increase in temperature moves the ferrite-austenite interface backwards and promotes detachment of the primary and secondary arms at the δ-γ interface via a reverse peritectic reaction. The results show a massive-like transformation inducing the dendrite arm fragmentation has a role in formation of the solidification structure and the austenite grain structures in the Fe-C alloys.

Crystal growth kinetics in undercooled melts of pure Ge, Si and Ge-Si alloys

We report on measurements of crystal growth dynamics in semiconducting pure Ge and pure Si melts and in Ge_100-x Si _x (x = 25, 50, 75) alloy melts as a function of undercooling. Electromagnetic levitation techniques are applied to undercool the samples in a containerless way. The growth velocity is measured by the utilization of a high-speed camera technique over an extended range of undercooling. Solidified samples are examined with respect to their microstructure by scanning electron microscopic investigations. We analyse the experimental results of crystal growth kinetics as a function of undercooling within the sharp interface theory developed by Peter Galenko. Transitions of the atomic attachment kinetics are found at large undercoolings, from faceted growth to dendrite growth.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

Dendrite fragmentation: an experiment-driven simulation

The processes leading to the fragmentation of secondary dendrite arms are studied using a three-dimensional Sn dendritic structure that was measured experimentally as an initial condition in a phase-field simulation. The phase-field model replicates the kinetics of the coarsening process seen experimentally. Consistent with the experiment, the simulations of the Sn-rich dendrite show that secondary dendrite arm coalescence is prevalent and that fragmentation is not. The lack of fragmentation is due to the non-axisymmetric morphology and comparatively small spacing of the dendrite arms. A model for the coalescence process is proposed, and, consistent with the model, the radius of the contact region following coalescence increases as t^1/3 We find that small changes in the width and spacing of the dendrite arms can lead to a very different fragmentation-dominated coarsening process. Thus, the alloy system and growth conditions of the dendrite can have a major impact on the fragmentation process.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

Combinatorial Strategies for Synthesis and Characterization of Alloy Microstructures over Large Compositional Ranges

The exploration of new alloys with desirable properties has been a long-standing challenge in materials science because of the complex relationship between composition and microstructure. In this Research Article, we demonstrate a combinatorial strategy for the exploration of composition dependence of microstructure. This strategy is comprised of alloy library synthesis followed by high-throughput microstructure characterization. As an example, we synthesized a ternary Au-Cu-Si composition library containing over 1000 individual alloys using combinatorial sputtering. We subsequently melted and resolidified the entire library at controlled cooling rates. We used scanning optical microscopy and X-ray diffraction mapping to explore trends in phase formation and microstructural length scale with composition across the library. The integration of combinatorial synthesis with parallelizable analysis methods provides a efficient method for examining vast compositional ranges. The availability of microstructures from this vast composition space not only facilitates design of new alloys by controlling effects of composition on phase selection, phase sequence, length scale, and overall morphology, but also will be instrumental in understanding the complex process of microstructure formation in alloys.

Detachment of secondary dendrite arm in a directionally solidified Sn-Ni peritectic alloy under deceleration growth condition

In order to better understand the detachment mechanism of secondary dendrite arm during peritectic solidification, the detachment of secondary dendrite arm from the primary dendrite arms in directionally solidified Sn-36at.%Ni peritectic alloys is investigated at different deceleration rates. Extensive detachment of secondary dendrite arms from primary stem is observed below peritectic reaction temperature TP. And an analytical model is established to characterize the detachment process in terms of the secondary dendrite arm spacing λ2, the root radius of detached arms and the specific surface area (SV) of dendrites. It is found that the detachment mechanism is caused by not only curvature difference between the tips and roots of secondary branches, but also that between the thicker secondary branches and the thinner ones. Besides, this detachment process is significantly accelerated by the temperature gradient zone melting (TGZM) effect during peritectic solidification. It is demonstrated that the reaction constant (f) which is used to characterize the kinetics of peritectic reaction is crucial for the determination of the detachment process. The value of f not only changes with growth rate but also with solidification time at a given deceleration rate. In conclusion, these findings help the better understanding of the detachment mechanism.

Dendrite fragmentation in alloy solidification due to sidearm pinch-off

Dendrite sidebranch detachment is an important fragmentation mechanism during the solidification of alloys. The detachment occurs at the junction between a sidearm and its parent stem. While this pinching process is driven by capillarity, the presence of solidification opposes the instability. Using a simple numerical model of a single sidearm, we are able to capture the essential dynamics of dendrite sidebranch development and the resulting morphological transitions. While shortly before pinch-off the neck itself obeys well-known universal scaling relations, the overall evolution of the sidearm shape sensitively depends on its initial geometry and the rate of solidification. It is found that pinch-off only occurs over limited ranges of geometrical parameters and cooling rates and is generally bounded by sidearm retraction and coalescence regimes. Simple scaling relations are identified that provide the bounds for the pinch-off regime. Pinching at the branching point is shown to be faster than the Rayleigh-Plateau instability of an infinitely long cylinder.

Thermo-solutal and kinetic regimes of an anisotropic dendrite growing under forced convective flow

A new selection criterion for the stable mode of anisotropic dendrite growing under forced convective flow in thermo-solutal and kinetic regimes is obtained.

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

We use a phase-field model for the growth of dendrites in dilute binary alloys under coupled thermosolutal control to explore the dependence of the dendrite tip velocity and radius of curvature upon undercooling, Lewis number (ratio of thermal to solutal diffusivity), alloy concentration, and equilibrium partition coefficient. Constructed in the quantitatively valid thin-interface limit, the model uses advanced numerical techniques such as mesh adaptivity, multigrid, and implicit time stepping to solve the nonisothermal alloy solidification problem for material parameters that are realistic for metals. From the velocity and curvature data we estimate the dendrite operating point parameter σ*. We find that σ* is nonconstant and, over a wide parameter space, displays first a local minimum followed by a local maximum as the undercooling is increased. This behavior is contrasted with a similar type of behavior to that predicted by simple marginal stability models to occur in the radius of curvature, on the assumption of constant σ*.

Experimental evidence for dendrite tip splitting in deeply undercooled, ultrahigh purity Cu

In a recent paper we used a phase-field model of solidification in deeply undercooled pure melts to show that a kinetic instability could result in dendrite tip splitting, and we speculated that such tip splitting could give rise to the phenomenon of spontaneous grain refinement. Here we present evidence, from the as-solidified microstructure of deeply undercooled ultrahigh purity Cu, of what appears to be dendrite tip splitting during recalescence. The significance of this finding in a nongrain refined sample is discussed in terms of the current theories for spontaneous grain refinement.